We have shown that the square-octagon, the kagomé, and the honeycomb lattices can exhibit observable EdH effect. The influence of a non-zero Berry curvature originating from DM interactions and its underlying topological identity is preserved even though the lattice structure changes. Thus, similar conclusions, not qualitatively differently, can be obtained from other lattices which can support a non-zero Berry curvature. Our conclusions should also hold for other recently studied systems such as the kagomé lattice [1]}, [2]}, the Lieb lattice [3]}, or the star lattice [4]}. It is also interesting to consider a model with two kinds of DM interaction, competing with each other on the square-octagon lattice. More precisely, the system should possess a broken up-down symmetry as in a ferro- or ferri- magnetic system. In antiferromagnets, the DM interaction can only result in the spin Nernst effect [5]}.
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